Rooney was not involved in United's surprise 1-0 defeat at Norwich City on Saturday after being laid low by tonsillitis.
He is due to be assessed by United on Sunday and Ferguson is keen to have the striker in his plans for Tuesday's group game in Turkey.
Ferguson said: "We hope he will be in on Sunday - we will see what he is like then.
"If he does [come in] hopefully we can get him ready for Tuesday."
Rooney had already been a doubt for the Red Devils' trip to Carrow Road after being forced to miss England's midweek friendly against Sweden due to an ankle injury suffered in the win at Aston Villa.
United are guaranteed a place in the last 16 of the Champions League after winning their opening four group fixtures and Ferguson is expected to rest several key players against Galatasaray.